Dosage math is one of the few places on shift where a small slip turns into a real error. The good news: almost everything you calculate at the bedside comes down to a handful of formulas. Here they are, each with a worked example you can copy the next time the numbers do not line up.
Start with one rule: keep your units
Most wrong answers are not math mistakes. They are unit mistakes, mg where you needed mcg, or minutes where the pump wanted hours. Before you calculate anything, convert everything into the same units and write them down. Three conversions cover almost every order:
- 1 g = 1,000 mg
- 1 mg = 1,000 mcg
- 1 kg = 2.2 lb
The core formula: desired over have
When you know the dose you want and the strength you have, use desired over have:
Amount to give = (Desired dose / Dose on hand) x the amount that dose comes in
Order: acetaminophen 650 mg by mouth. You have 325 mg tablets.
650 / 325 x 1 tablet = 2 tablets.
The same formula works for liquids. Order: 500 mg, and the bottle reads 250 mg per 5 mL.
500 / 250 x 5 mL = 10 mL.
When a fraction feels easy to flip: dimensional analysis
Dimensional analysis gives the same answer with a built-in check. You line up the units so the ones you do not want cancel, and the unit you need is what survives.
Order: heparin 5,000 units subcut. Vial: 10,000 units per mL.
5,000 units x (1 mL / 10,000 units) = 0.5 mL. The units cancel, mL is left, and 0.5 mL is your answer.
Weight-based dosing, and the safe-dose check
Many drugs are ordered per kilogram. Convert pounds to kilograms first, then multiply.
Order: 15 mg/kg for an 80 kg patient.
15 mg x 80 = 1,200 mg.
Weight-based orders are also where you catch a bad order. If a reference lists a safe range of 25 to 50 mg/kg/day for a 20 kg child, that is 500 to 1,000 mg/day. An order for 750 mg/day sits inside the range. An order for 1,500 mg/day does not, and that is your cue to call before you give it.
IV flow rate: how many mL per hour
mL/hr = total volume (mL) / time (hr)
Order: 1,000 mL over 8 hours.
1,000 / 8 = 125 mL/hr. That is the number you set on the pump.
How long will this bag run?
Flip the same formula when you want to know when to be back in the room.
Time (hr) = volume (mL) / rate (mL/hr)
A 500 mL bag running at 125 mL/hr lasts 4 hours.
IV drip rate: how many drops per minute
When you are counting drops instead of using a pump, you need the tubing drop factor, printed on the package.
gtt/min = (volume in mL x drop factor in gtt/mL) / time in minutes
- Macrodrip tubing: 10, 15, or 20 gtt/mL
- Microdrip tubing: 60 gtt/mL
Order: 1,000 mL over 8 hours with 15 gtt/mL tubing. Put the time in minutes (8 x 60 = 480).
(1,000 x 15) / 480 = 31 gtt/min.
Microdrip example: 50 mL over 30 minutes with 60 gtt/mL tubing.
(50 x 60) / 30 = 100 gtt/min.
Titrated drips: mcg/kg/min to a pump rate
Pressors and sedation are usually ordered in mcg/kg/min, but the pump wants mL/hr. Bring the dose to an hourly amount, then divide by how concentrated the bag is.
mL/hr = (dose in mcg/kg/min x weight in kg x 60) / concentration in mcg/mL
Order: dopamine 5 mcg/kg/min for an 80 kg patient. Bag: 400 mg in 250 mL.
First the concentration: 400 mg = 400,000 mcg, divided by 250 mL = 1,600 mcg/mL.
(5 x 80 x 60) / 1,600 = 24,000 / 1,600 = 15 mL/hr.
Work it in that order every time and the units take care of themselves.
Reconstituted and powdered meds
For a drug you mix yourself, read the final concentration off the vial after reconstitution, not the powder amount, then run desired over have on that number. If a vial reconstitutes to 1 g per 4 mL and the order is 500 mg, that is 500 / 1,000 x 4 mL = 2 mL.
Quick conversions to keep on your sheet
| From | To |
|---|---|
| 1 g | 1,000 mg |
| 1 mg | 1,000 mcg |
| 1 kg | 2.2 lb |
| 1 L | 1,000 mL |
| 1 tsp | 5 mL |
| 1 tbsp | 15 mL |
| 1 oz | 30 mL |
A word on rounding
You cannot count a fraction of a drop, so round gtt/min to a whole number. Pump rates in mL/hr follow your pump, some take tenths, some do not. And be suspicious of any answer that asks you to split an unscored tablet or give more than two or three tablets at once. That is usually a units error upstream, not the plan.
The habits that prevent the error
- Convert to one set of units before you touch the numbers.
- Ask whether the answer is reasonable. Two tablets is normal. Twelve is not.
- For high-alert drugs like heparin, insulin, opioids, pressors, and chemotherapy, get an independent double check, a second nurse who calculates it without seeing your answer.
- When an order and the safe range disagree, stop and call. Being right is worth the page.
None of this replaces your pharmacy or your facility protocol. Verify high-alert medications and anything that does not sit right before you give it.
Keep the weights, rates, and times you are trending in one place instead of on your glove. A free nursing brain sheet gives you a spot for them alongside the rest of your shift, and the rights of medication administration cover the checks that go around the math.
Sources: standard nursing dosage references for the desired-over-have, IV flow-rate, drip-rate, and mcg/kg/min formulas, including SimpleNursing, Mometrix, and the open-access WTCS Nursing Dosage Calculations text. Always follow your facility protocol and pharmacy.